Sweet exponential decay
by Irini Perissinaki
We say that a quantity is decaying exponentially when it decreases at a rate proportional to its current value. Another way to think of the exponential decay is that the time required for the decaying quantity to fall to one half of its initial value is fixed and independent of the initial amount. This time is called "Half-Life". Most common examples of exponentially decaying quantities are the radio active isotopes. For instance, let's take the radio active phosphorus-32: its half-life is about 14 days which means that if we have an initial amount of Phosphorus-32, say Q0, then, after 14 days the amount left will be ½Q0. In the school book there is a small list of radioactive isotopes and their half-life, which we include below.
The sweet experiment
It is really thrilling when the school-algebra meets some applications in the real world, as in the case of the exponential decay. But is it only a piece of information? How could we activate our students to experiment with quantities decaying exponentially and to make them derive the correct rate of decaying? I got my answer from a fellow teacher, Pota Kotarinou, who wrote a wonderful teaching senario titled "The chocolates and the exponential rate law". This was the senario we applied in class with two groups: B2 and B3 on the 4th of April 2016.
The experiment was organised in 7 stages:
Presenting our work
Find below some descriptive slides and the completed worksheets of each team.
Completed team worksheets
Extra teaching material used for the lesson
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